Evaluating bias control strategies in observational studies using frequentist model averaging

Estimating a treatment effect from observational data requires modeling treatment and outcome subject to uncertainty/misspecification. A previous research has shown that it is not possible to find a uniformly best strategy. In this article we propose a novel Frequentist Model Averaging (FMA) framework encompassing any estimation strategy and accounting for model uncertainty by computing a cross-validated estimate of Mean Squared Prediction Error (MSPE). We present a simulation study with data mimicking an observational database. Model averaging over 15+ strategies was compared with individual strategies as well as the best strategy selected by minimum MSPE. FMA showed robust performance (Bias, Mean Squared Error (MSE), and Confidence Interval (CI) coverage). Other strategies, such as linear regression, did well in simple scenarios but were inferior to the FMA in a scenario with complex confounding.